Field of the Invention
The present invention concerns a method for acquiring magnetic resonance image data that is entered into k-space at sample points in k-space with a random undersampling scheme, as well as a magnetic resonance tomography apparatus for implementing such a method.
Description of the Prior Art
Magnetic resonance tomography (MRT) is an imaging method that enables the acquisition of two-dimensional or three-dimensional image data sets that can depict structures inside an examined person with high resolution. In MRT, the magnetic moments of protons in an examination subject are aligned in a basic magnetic field or primary magnetic field (B0) so that a macroscopic magnetization arises. This is subsequently deflected out of the steady state, parallel to the basic magnetic field, via the radiation of radio-frequency (RF) pulses. Special RF transmission coils are typically used for radiation.
The decay of the excited magnetization back into the steady state or the magnetization dynamic is subsequently detected by means of one or more RF reception coils. A spatial coding of the acquired magnetic resonance (MR) data is hereby achieved via the application of various magnetic field gradients (for slice selection, phase coding or frequency coding). The data that are acquired and spatially resolved in such a manner initially exist in a spatial frequency domain (k-space) and can be transformed into the spatial domain (image space) via a subsequent Fourier transformation. K-space can be scanned with different trajectories by the targeted switching (activation) of the magnetic field gradients, wherein a conventional scanning includes the successive acquisition of frequency-coded k-space lines (that are generally oriented along the x-axis of k-space) for different phase codings (that define the y-axis of k-space).
In order to reduce the acquisition duration—for example in the acquisition of MR data of a freely breathing examination subject—different methods are proposed that, on the one hand, enable an acceleration of the acquisition by the parallel usage of multiple coils with respectively limited field of view; on the other hand, they undersample k-space, i.e. omit k-space lines or individual k-space points that are to be sampled, for example. Examples of such techniques are the “Generalized Auto-Calibrating Partial [sic] Parallel Acquisition” (GRAPPA), “Sensitivity Encoding” (SENSE) and “Simultaneous Acquisition of Spatial Harmonics” (SMASH) imaging methods, which are also generally designated as partially parallel acquisition (ppa) methods. These and further methods are known from “SMASH, SENSE, PILS, GRAPPA” by M. Blaimer et al. in Top. Magn. Reson. Imaging 15 (2004), 223, for example.
In general, the undersampling of k-space takes place by means of a ppa method according to the requirements of an undersampling scheme for various sampling points. Reduced MR data are acquired for these sampling points with multiple different RF reception coils. The missing data—i.e. unsampled k-space points, for example—are reconstructed directly or indirectly from the correlation between the reduced MR data of the various RF reception coils, such that reconstructed MR data are obtained from the reduced MR data. These no longer have omitted k-space points. For this purpose, an anti-aliasing (in image space, for instance) of the superimposed, reduced MR data of the various RF reception coils and/or a reconstruction kernel that is applied to the reduced MR data can be used. For example, in GRAPPA-like methods, a reconstruction kernel can be used; in SENSE-like methods, the model assumption can be used that each coil image can be described as a product of magnetization image and coil sensitivity. Particularly in GRAPPA-like ppa methods, the reconstructed MR data can exist for every RF reception coil. However, a single accelerated data set—known as accelerated MR data—can be obtained from the reconstructed MR data. An MR image which can be used for medical diagnosis or to determine physical measurement values (volumes of organs etc.), for example, can be directly obtained from the accelerated MR data. In SENSE-like ppa methods, for example, the reconstructed MR data can already be present as an MR image in image space. It should be understood that the different MR data—i.e. reduced, reconstructed and accelerated data—can have different information levels or, respectively, can respectively be shown in image or positional frequency space depending on the specific type of ppa acquisition method (for example SENSE or GRAPPA). The corresponding techniques are known to those skilled in the art, such that it is not necessary to present details more closely here.
In general, different reconstruction algorithms allow a random undersampling scheme in which the sample points are randomly or statistically distributed in k-space, for example. This in particular applies to “Conjugate Gradient SENSE” (CG-SENSE), which is an extended PPA acquisition method building on conventional SENSE. Details in this regard are known from “Advances in Sensitivity Encoding With Arbitrary Space Trajectories” by K. P. Pruessmann et al., Mag. Reson. Med. 46 (2001) 638-651. Furthermore, an undersampling by means of the SPIRIT method is known; see in this regard “SPIRiT: Iterative self-consistent parallel imaging reconstruction from arbitrary k-space” by M. Lustig and J. M. Paul in Mag. Reson. Med. 64 (2010) 457-471. For example, it is possible to create random undersampling schemes by means of the Poisson disc distribution. The Poisson disc technique designates a known method that allows sample points of the undersampling scheme to be selected such that they have a statistical distribution and such that it is simultaneously ensured that adjacent sample points do not fall below a minimum distance, at least on average. An undersampling scheme with uniformly and randomly distributed sample points is achieved as a result.
Ppa methods are characterized by a phenomenon known as noise amplification. This means that the noise in the MR images (image noise) can be greater than the signal noise in the raw MR data (thus the reduced MR data). In particular, the reconstructed MR data can have relatively large physical uncertainties or errors (thus signal noise) since the application of the reconstruction kernel can amplify the noise. For example, the noise of the reconstructed MR data can be proportional or equal to the image noise. The image noise is a technically relevant parameter. It is significant for the quality of the MRT result and can allow diagnostics or continuative processing with determinable uncertainties or confidence values to be implemented using the MR images.
In principle, the calculation of the noise amplification (i.e. the calculation of the image noise) for an undersampling scheme is possible; see in this regard Equation 20 from “SENSE: Sensitivity Encoding for FAST MRI” by K. P. Pruessmann et al. in Mag. Reson. Med. 42 (1999) 952-962, for instance. However, such a calculation is numerically complex and requires the inversion of a matrix with the dimension of the complete k-space. Therefore, in practice it can also be possible to a limited extent to evaluate a specific undersampling scheme in this regard before acquisition of the reduced MR data and reconstruction of the reconstructed MR data. Computing capacities and available computing time can be limited in practice. Moreover, conventional ppa methods have the disadvantage that no optimization or only a slight optimization with regard to the reduced image noise is possible based on the hard-set undersampling scheme, or an undersampling scheme created according to fixed statistical criteria (for example Poisson disc distribution). With such an undersampling, in practice, parameters are absent which could be optimized with regard to a reduction of the image noise.